Scheduling of pipelined operator graphs

Bodlaender, Hans L.; Schuurman, Petra; Woeginger, Gerhard J.

doi:10.1007/s10951-011-0225-1

Cited by 8 publications

(5 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Given as input an edge-weighted graph G = (V, E), k ∈ N + , d ≥ 2 and an arbitrarily small error parameter > 0, our algorithm is able to return a set K, such that any v, u ∈ K are at distance d(v, u) ≥ d 1+ , in time O * ((tw/ ) O(tw) ), if G has a d-scattered set of size |K|. Our algorithm makes use of a technique introduced in [24] (originally used in [7], see also [1,22]) for approximating problems that are W-hard by treewidth. If the hardness of the problem arises from the need of the dynamic programming table to store tw large numbers (in our case, the distances of the vertices in the bag from the closest selection), we can significantly speed up the algorithm by replacing all values by the closest integer power of (1 + δ), for some appropriately chosen δ, thus reducing the table size from d tw to (log (1+δ) d) tw .…”

Section: Tree-depth: Tight Eth Lower Boundmentioning

confidence: 99%

Structurally Parameterized d-Scattered Set

Katsikarelis¹,

Lampis²,

Paschos³

2018

Graph-Theoretic Concepts in Computer Science

View full text Add to dashboard Cite

In d-Scattered Set we are given an (edge-weighted) graph and are asked to select at least k vertices, so that the distance between any pair is at least d, thus generalizing Independent Set. We provide upper and lower bounds on the complexity of this problem with respect to various standard graph parameters. In particular, we show the following:• For any d ≥ 2, an O * (d tw )-time algorithm, where tw is the treewidth of the input graph and a tight SETH-based lower bound matching this algorithm's performance. These generalize known results for Independent Set.• d-Scattered Set is W[1]-hard parameterized by vertex cover (for edge-weighted graphs), or feedback vertex set (for unweighted graphs), even if k is an additional parameter.• A single-exponential algorithm parameterized by vertex cover for unweighted graphs, complementing the above-mentioned hardness.• A 2 O(td 2 ) -time algorithm parameterized by tree-depth (td), as well as a matching ETHbased lower bound, both for unweighted graphs.We complement these mostly negative results by providing an FPT approximation scheme parameterized by treewidth. In particular, we give an algorithm which, for any error parameter > 0, runs in time O * ((tw/ ) O(tw) ) and returns a d/(1+ )-scattered set of size k, if a d-scattered set of the same size exists. IntroductionIn this paper we study the d-Scattered Set problem: given graph G = (V, E) and a metric weight function w : E → N + that gives the length of each edge, we are asked if there exists a set K of at least k selections from V , such that the distance between any pair v, u ∈ K is at least d(v, u) ≥ d, where d(v, u) denotes the shortest-path distance from v to u under weight function w. If w assigns weight 1 to all edges, the variant is called unweighted.The problem can already be seen to be hard, as it generalizes Independent Set (for d = 2), even to approximate (under standard complexity assumptions), i.e. the optimal k cannot be approximated to n 1− in polynomial time [19], while an alternative name is 28,13]. This hardness prompts the analysis of the problem when the input graph is of restricted structure, our aim being to provide a comprehensive account of the complexity of d-Scattered Set through various upper and lower bound results. Our viewpoint is parameterized: we consider the well-known structural parameters treewidth tw, tree-depth td, vertex cover number vc and feedback vertex set number fvs, that comprehensively express the intended restrictions on the input graph's structure (as they range in size and applicability), while we examine both the edge-weighted and unweighted variants of the problem. 1

show abstract

Section: Tree-depth: Tight Eth Lower Boundmentioning

confidence: 99%

Structurally Parameterized d-Scattered Set

Katsikarelis¹,

Lampis²,

Paschos³

2018

Graph-Theoretic Concepts in Computer Science

View full text Add to dashboard Cite

show abstract

“…The optimization target of some scheduling problem [1], [4], [5] is to find a schedule with minimum response time (or makespan). The response time of a schedule is the maximum processor load.…”

Section: Related Workmentioning

confidence: 99%

“…. , p} by means of dynamic programming similar to [1], [3], [5]. The details of computing S (T v , k) are described briefly as follows.…”

Section: Definition 4 (Near K-[l U]partition)mentioning

confidence: 99%

“…We start from the first element of A (denoted by A [1]) and compute the sum of A [1] [2] for new iteration, until we finish the computing at the last element of A.…”

Section: Obviously S (Tmentioning

confidence: 99%

“…Pipelined operator scheduling is an important problem in the area of parallel and distributed computing [1], [2]. For a large class of applications, the computing tasks can be represented as pipelined operator graphs, and an efficient operator schedule is critical to reach the best possible performance for distributed computing.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An Efficient Algorithm for Node-Weighted Tree Partitioning with Subtrees' Weights in a Given Range

Luo

Chen

et al. 2013

IEICE Trans. Inf. & Syst.

View full text Add to dashboard Cite

SUMMARYTree partitioning arises in many parallel and distributed computing applications and storage systems. Some operator scheduling problems need to partition a tree into a number of vertex-disjoint subtrees such that some constraints are satisfied and some criteria are optimized. Given a tree T with each vertex or node assigned a nonnegative integer weight, two nonnegative integers l and u (l < u), and a positive integer p, we consider the following tree partitioning problems: partitioning T into minimum number of subtrees or p subtrees, with the condition that the sum of node weights in each subtree is at most u and at least l. To solve the two problems, we provide a fast polynomial-time algorithm, including a preprocessing method and another bottom-up scheme with dynamic programming. With experimental studies, we show that our algorithm outperforms another prior algorithm presented by Ito et al. greatly.

show abstract

Balanced Partitions of Trees and Applications

Feldmann

Foschini

2013

Algorithmica

View full text Add to dashboard Cite

We study the k-BALANCED PARTITIONING problem in which the vertices of a graph are to be partitioned into k sets of size at most n/k while minimising the cut size, which is the number of edges connecting vertices in different sets. The problem is well studied for general graphs, for which it cannot be approximated within any factor in polynomial time. However, little is known about restricted graph classes. We show that for trees k-BALANCED PARTITIONING remains surprisingly hard. In particular, approximating the cut size is APX-hard even if the maximum degree of the tree is constant. If instead the diameter of the tree is bounded by a constant, we show that it is NP-hard to approximate the cut size within n c , for any constant c < 1. In the face of the hardness results, we show that allowing near-balanced solutions, in which there are at most (1 + ε) n/k vertices in any of the k sets, admits a PTAS for trees. Remarkably, the computed cut size is no larger than that of an optimal balanced solution. In the final section of our paper, we harness results on embedding graph metrics into tree metrics to extend our PTAS for trees to general graphs. In addition to being conceptually simpler and easier to analyse, our scheme improves the best factor known on the cut size of near-balanced solutions from O(log 1.5 (n)/ε 2 ) [Andreev and Räcke TCS 2006] to O(log n), for weighted graphs. This also settles a question posed by Andreev and Räcke of whether an algorithm with approximation guarantees on the cut size independent from ε exists.

show abstract

Scheduling of pipelined operator graphs

Cited by 8 publications

References 15 publications

Structurally Parameterized d-Scattered Set

Structurally Parameterized d-Scattered Set

An Efficient Algorithm for Node-Weighted Tree Partitioning with Subtrees' Weights in a Given Range

Balanced Partitions of Trees and Applications

Contact Info

Product

Resources

About